SRC/zhegvd.f(3)

NAME
SRC/zhegvd.f

SYNOPSIS

  Functions/Subroutines
subroutine zhegvd (itype, jobz, uplo, n, a, lda, b, ldb, w, work, lwork, rwork, lrwork, iwork, liwork, info)
ZHEGVD

Function/Subroutine Documentation

  subroutine zhegvd (integer itype, character jobz, character uplo, integer n, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( ldb, * ) b, integer ldb, double precision, dimension( * ) w, complex*16, dimension( * ) work, integer lwork, double precision, dimension( * ) rwork, integer lrwork, integer, dimension( * ) iwork, integer liwork, integer info)

ZHEGVD

Purpose:

    !>
    !> ZHEGVD computes all the eigenvalues, and optionally, the eigenvectors
    !> of a complex generalized Hermitian-definite eigenproblem, of the form
    !> A*x=(lambda)*B*x,  A*Bx=(lambda)*x,  or B*A*x=(lambda)*x.  Here A and
    !> B are assumed to be Hermitian and B is also positive definite.
    !> If eigenvectors are desired, it uses a divide and conquer algorithm.
    !>
    !>

Parameters
    ITYPE

    !>          ITYPE is INTEGER
    !>          Specifies the problem type to be solved:
    !>          = 1:  A*x = (lambda)*B*x
    !>          = 2:  A*B*x = (lambda)*x
    !>          = 3:  B*A*x = (lambda)*x
    !>

    JOBZ

    !>          JOBZ is CHARACTER*1
    !>          = 'N':  Compute eigenvalues only;
    !>          = 'V':  Compute eigenvalues and eigenvectors.
    !>

    UPLO

    !>          UPLO is CHARACTER*1
    !>          = 'U':  Upper triangles of A and B are stored;
    !>          = 'L':  Lower triangles of A and B are stored.
    !>

    N

    !>          N is INTEGER
    !>          The order of the matrices A and B.  N >= 0.
    !>

    A

    !>          A is COMPLEX*16 array, dimension (LDA, N)
    !>          On entry, the Hermitian matrix A.  If UPLO = 'U', the
    !>          leading N-by-N upper triangular part of A contains the
    !>          upper triangular part of the matrix A.  If UPLO = 'L',
    !>          the leading N-by-N lower triangular part of A contains
    !>          the lower triangular part of the matrix A.
    !>
    !>          On exit, if JOBZ = 'V', then if INFO = 0, A contains the
    !>          matrix Z of eigenvectors.  The eigenvectors are normalized
    !>          as follows:
    !>          if ITYPE = 1 or 2, Z**H*B*Z = I;
    !>          if ITYPE = 3, Z**H*inv(B)*Z = I.
    !>          If JOBZ = 'N', then on exit the upper triangle (if UPLO='U')
    !>          or the lower triangle (if UPLO='L') of A, including the
    !>          diagonal, is destroyed.
    !>

    LDA

    !>          LDA is INTEGER
    !>          The leading dimension of the array A.  LDA >= max(1,N).
    !>

    B

    !>          B is COMPLEX*16 array, dimension (LDB, N)
    !>          On entry, the Hermitian matrix B.  If UPLO = 'U', the
    !>          leading N-by-N upper triangular part of B contains the
    !>          upper triangular part of the matrix B.  If UPLO = 'L',
    !>          the leading N-by-N lower triangular part of B contains
    !>          the lower triangular part of the matrix B.
    !>
    !>          On exit, if INFO <= N, the part of B containing the matrix is
    !>          overwritten by the triangular factor U or L from the Cholesky
    !>          factorization B = U**H*U or B = L*L**H.
    !>

    LDB

    !>          LDB is INTEGER
    !>          The leading dimension of the array B.  LDB >= max(1,N).
    !>

    W

    !>          W is DOUBLE PRECISION array, dimension (N)
    !>          If INFO = 0, the eigenvalues in ascending order.
    !>

    WORK

    !>          WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
    !>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
    !>

    LWORK

    !>          LWORK is INTEGER
    !>          The length of the array WORK.
    !>          If N <= 1,                LWORK >= 1.
    !>          If JOBZ  = 'N' and N > 1, LWORK >= N + 1.
    !>          If JOBZ  = 'V' and N > 1, LWORK >= 2*N + N**2.
    !>
    !>          If LWORK = -1, then a workspace query is assumed; the routine
    !>          only calculates the optimal sizes of the WORK, RWORK and
    !>          IWORK arrays, returns these values as the first entries of
    !>          the WORK, RWORK and IWORK arrays, and no error message
    !>          related to LWORK or LRWORK or LIWORK is issued by XERBLA.
    !>

    RWORK

    !>          RWORK is DOUBLE PRECISION array, dimension (MAX(1,LRWORK))
    !>          On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK.
    !>

    LRWORK

    !>          LRWORK is INTEGER
    !>          The dimension of the array RWORK.
    !>          If N <= 1,                LRWORK >= 1.
    !>          If JOBZ  = 'N' and N > 1, LRWORK >= N.
    !>          If JOBZ  = 'V' and N > 1, LRWORK >= 1 + 5*N + 2*N**2.
    !>
    !>          If LRWORK = -1, then a workspace query is assumed; the
    !>          routine only calculates the optimal sizes of the WORK, RWORK
    !>          and IWORK arrays, returns these values as the first entries
    !>          of the WORK, RWORK and IWORK arrays, and no error message
    !>          related to LWORK or LRWORK or LIWORK is issued by XERBLA.
    !>

    IWORK

    !>          IWORK is INTEGER array, dimension (MAX(1,LIWORK))
    !>          On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
    !>

    LIWORK

    !>          LIWORK is INTEGER
    !>          The dimension of the array IWORK.
    !>          If N <= 1,                LIWORK >= 1.
    !>          If JOBZ  = 'N' and N > 1, LIWORK >= 1.
    !>          If JOBZ  = 'V' and N > 1, LIWORK >= 3 + 5*N.
    !>
    !>          If LIWORK = -1, then a workspace query is assumed; the
    !>          routine only calculates the optimal sizes of the WORK, RWORK
    !>          and IWORK arrays, returns these values as the first entries
    !>          of the WORK, RWORK and IWORK arrays, and no error message
    !>          related to LWORK or LRWORK or LIWORK is issued by XERBLA.
    !>

    INFO

    !>          INFO is INTEGER
    !>          = 0:  successful exit
    !>          < 0:  if INFO = -i, the i-th argument had an illegal value
    !>          > 0:  ZPOTRF or ZHEEVD returned an error code:
    !>             <= N:  if INFO = i and JOBZ = 'N', then the algorithm
    !>                    failed to converge; i off-diagonal elements of an
    !>                    intermediate tridiagonal form did not converge to
    !>                    zero;
    !>                    if INFO = i and JOBZ = 'V', then the algorithm
    !>                    failed to compute an eigenvalue while working on
    !>                    the submatrix lying in rows and columns INFO/(N+1)
    !>                    through mod(INFO,N+1);
    !>             > N:   if INFO = N + i, for 1 <= i <= N, then the leading
    !>                    principal minor of order i of B is not positive.
    !>                    The factorization of B could not be completed and
    !>                    no eigenvalues or eigenvectors were computed.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Further Details:

    !>
    !>  Modified so that no backsubstitution is performed if ZHEEVD fails to
    !>  converge (NEIG in old code could be greater than N causing out of
    !>  bounds reference to A - reported by Ralf Meyer).  Also corrected the
    !>  description of INFO and the test on ITYPE. Sven, 16 Feb 05.
    !>

Contributors:
    Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA

Definition at line 241 of file zhegvd.f.

Author

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